{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multivariate Gaussian Random Walk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.linalg import cholesky\n",
    "\n",
    "import pymc3 as pm\n",
    "import theano\n",
    "\n",
    "np.random.seed(42)\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulate the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "D = 3\n",
    "N = 300\n",
    "sections = 5\n",
    "period = N/sections\n",
    "\n",
    "Sigma_a = np.random.randn(D, D)\n",
    "Sigma_a = Sigma_a.T.dot(Sigma_a)\n",
    "L_a = cholesky(Sigma_a, lower=True)\n",
    "\n",
    "Sigma_b = np.random.randn(D, D)\n",
    "Sigma_b = Sigma_b.T.dot(Sigma_b)\n",
    "L_b = cholesky(Sigma_b, lower=True)\n",
    "\n",
    "# Gaussian Random walk:\n",
    "alpha = np.cumsum(L_a.dot(np.random.randn(D, sections)), axis=1).T\n",
    "beta = np.cumsum(L_b.dot(np.random.randn(D, sections)), axis=1).T\n",
    "sigma = 0.1\n",
    "\n",
    "t = np.arange(N)[:, None]/ N\n",
    "alpha = np.repeat(alpha, period, axis=0)\n",
    "beta = np.repeat(beta, period, axis=0)\n",
    "y = alpha + beta*t + sigma*np.random.randn(N, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 5))\n",
    "plt.plot(t, y)\n",
    "plt.title('Three Correlated Series')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Scaler():\n",
    "    def __init__(self):\n",
    "        mean_ = None\n",
    "        std_ = None\n",
    "    \n",
    "    def transform(self, x):\n",
    "        return (x - self.mean_) / self.std_\n",
    "    \n",
    "    def fit_transform(self, x):\n",
    "        self.mean_ = x.mean(axis=0)\n",
    "        self.std_ = x.std(axis=0)\n",
    "        return self.transform(x)\n",
    "    \n",
    "    def inverse_transform(self, x):\n",
    "        return x*self.std_ + self.mean_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inference(t, y, sections, n_samples=100):\n",
    "    N, D = y.shape\n",
    "    \n",
    "    # Standardies y and t\n",
    "    y_scaler = Scaler()\n",
    "    t_scaler = Scaler()\n",
    "    y = y_scaler.fit_transform(y)\n",
    "    t = t_scaler.fit_transform(t)\n",
    "    # Create a section index\n",
    "    t_section = np.repeat(np.arange(sections), N/sections)\n",
    "    \n",
    "    # Create theano equivalent\n",
    "    t_t = theano.shared(np.repeat(t, D, axis=1))\n",
    "    y_t = theano.shared(y)\n",
    "    t_section_t = theano.shared(t_section)\n",
    "\n",
    "    with pm.Model() as model:\n",
    "        packed_L_α = pm.LKJCholeskyCov('packed_L_α', n=D,   \n",
    "                                 eta=2., sd_dist=pm.HalfCauchy.dist(2.5))\n",
    "        L_α = pm.expand_packed_triangular(D, packed_L_α)\n",
    "\n",
    "        packed_L_β = pm.LKJCholeskyCov('packed_L_β', n=D,   \n",
    "                                 eta=2., sd_dist=pm.HalfCauchy.dist(2.5))\n",
    "        L_β = pm.expand_packed_triangular(D, packed_L_β)\n",
    "\n",
    "        α = pm.MvGaussianRandomWalk('alpha', shape=(sections, D), chol=L_α)\n",
    "        β = pm.MvGaussianRandomWalk('beta', shape=(sections, D), chol=L_β)\n",
    "        alpha_r = α[t_section_t]\n",
    "        beta_r = β[t_section_t]\n",
    "        regression = alpha_r+beta_r*t_t\n",
    "\n",
    "        sd = pm.Uniform('sd', 0, 1)\n",
    "        likelihood = pm.Normal('y', mu=regression, sigma=sd, observed=y_t)\n",
    "        trace = pm.sample(n_samples, cores=4)\n",
    "\n",
    "    return trace, y_scaler, t_scaler, t_section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Only 100 samples in chain.\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [sd, beta, alpha, packed_L_β, packed_L_α]\n",
      "Sampling 4 chains: 100%|██████████| 2400/2400 [01:17<00:00, 19.88draws/s]\n"
     ]
    }
   ],
   "source": [
    "trace, y_scaler, t_scaler, t_section = inference(t, y, sections)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predict the mean expected y value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_mean = trace['alpha'][-1000:].mean(axis=0)\n",
    "b_mean = trace['beta'][-1000:].mean(axis=0)\n",
    "\n",
    "y_pred = y_scaler.inverse_transform(a_mean[t_section] + b_mean[t_section]*t_scaler.transform(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 5))\n",
    "plt.gca().set_prop_cycle('color', ['red', 'green', 'blue'])\n",
    "plt.plot(t, y, '.')\n",
    "plt.plot(t, y_pred)\n",
    "plt.title('Mean Prediction of Three Correlated Series')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
